Aniekan A. Ebiefung

The generalized Leontief input-output model and its application to the choice of new technology

The Leontief input-output model is generalized and formulated as a generalized linear complementarity problem. Conditions for existence of solutions are given, and solution techniques are reviewed. An application of the model to choosing new technologies is suggested.

Human factors affecting the success of advanced manufacturing systems

This paper analyzes the data collected from 98 manufacturing companies to investigate the associations between human factors and the success of advanced manufacturing systems (AMS). The AMS measures and human factors were cross-tabulated and the Chi Square values were used to test the hypotheses of the study. The results show that statistically significant, positive associations exit between human factors and the success of AMS implementation. The implications of the findings to the practitioners and researchers are discussed.

Existence theory and Q-matrix characterization for the generalized linear complementarity problem

Abstract Necessary and sufficient conditions for existence of solutions and a characterization of the set of Q -matrices for the generalized linear complementarity problem (GLCP) are presented. The results lead to an algorithm for solving the GLCP for any general vertical block matrix and provide an insight into the geometry of the problem. It is also shown that the GLCP is NP-complete in the case of a general vertical block matrix.

The Generalized Linear Complementarity Problem: Least Element Theory andZ-Matrices

Existence of solutions to the Generalized Linear Complementarity Problem (GLCP) is characterized when the associated matrix is a vertical blockZ-matrix. It is shown that if solutions exist, then one must be the leastelement of the feasible region. Moreover, the vertical block Z-matrixbelongs to the class of matrices where feasibility implies existence of asolution to the GLCP. The concept of sufficient matrices of class Z isinvestigated to obtain additional properties of the solution set.

Nonlinear mappings associated with the generalized linear complementarity problem

We show that the Cottle—Dantzig generalized linear complementarity problem (GLCP) is equivalent to a nonlinear complementarity problem (NLCP), a piecewise linear system of equations (PLS), a multiple objective programming problem (MOP), and a variational inequalities problem (VIP). On the basis of these equivalences, we provide an algorithm for solving problem GLCP.

Generalized P0- and Z-matrices

Abstract The concept of vertical block matrix introduced in generalized linear complementarity theory is studied within the matrix classes P0 and Z. Classical results of Fiedler and Ptak are extended, and relationships with existing results derived. Potential applications abound in economics, operations research, engineering, and physical sciences.

A support submatrix for the generalized linear complementarity problem

Abstract We provide an algorithm that selects, in a polynomial time, a representative submatrix whose appropriately defined LCP solution solves the GLCP. An algorithm based on support submatrices is also presented.

Production Equilibrium Point in Multi-Unit Manufacturing Systems and The Vertical Linear Complementarity Problem

A model that selects and produces products at an equilibrium point in multi-unit manufacturing systems is presented. It enables each business subsystem in the company to select and produce products so that the whole organization meets both internal and external demands at minimum inventory cost. Unlike previously proposed models, this model does not place any restrictions on the number of products or services that each business subsystem can provide. Proofs are provided to show existence of solutions and solvability, and a numerical example is given to demonstrate the utility of the model.

New perturbation results for solving the linear complementarity problem with Po-matrices☆

Abstract We provide new conditions under which the linear complementarity problem (LCP) can be solved by a perturbation method when the associated matrix is a P o -matrix. The new conditions apply to both degenerate and nondegenerate LCPs. Moreover, these conditions do not require that the P o -matrix belong to another matrix class such as, for example, the R o -matrix class.

An algorithm to solve the generalized linear complementarity problem with a vertical block z-matrix

Chandrasekarans algorithm for solving the linear complementarity problem with a Z-matrix is extended to solve the Generalized Linear Complementarity Problem (GLCP) when the is a vertical block Z-matrix of type (m 1,…,m n). The extended scheme solves the GLCP in at most n cycles by either finding a solution or declaring that none exists. Numerical examples are given to demonstrate the effectiveness of the algorithm